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C2×AGL(1,𝔽7)×C4⋊(C3⋊D3) #72245654

order6048
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×AGL(1,𝔽7)×C4⋊(C3⋊D3)

Splittings

FittingC2×C32×C4×C7 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C22×C3×C4⋊(C3⋊D3)

Subgroups

subgroupG/H
centerC22C2×C3⋊D3×AGL(1,𝔽7)
commutator, cosocleC2×C32×C7C24×C3
FrattiniC2C22×C3⋊D3×AGL(1,𝔽7)
FittingC2×C32×C4×C7C22×C3
socleC22×C32×C7C23×C3
hypercenterC2×C4C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C2×C4

3264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64083, AGL(1,𝔽7)×#64149
maximal normal subgroup ofC2×D4×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64083, AGL(1,𝔽7)×#64149
maximal quotient ofAGL(1,𝔽7)×#64083

GAP

Past the SmallGroups library coverage — no SmallGroups id.